Use of prior knowledge to inform restoration projects in estuaries of GOM

# randomize author order
aut <- c('Marcus Beck', 'Kirsten Dorans', 'Jessica Renee Henkel', 'Kathryn Ireland', 'Ed Sherwood', 'Patricia Varela') %>% 
  sample %>% 
  paste(collapse = ', ')

By Kirsten Dorans, Jessica Renee Henkel, Patricia Varela, Ed Sherwood, Kathryn Ireland, Marcus Beck

• https://fawda123.github.io/oss2017_synthesis/presentations/final_pres-figure/bayes_network.html

• Synthesize data in space and time to evaluate cumulative effects of restoration projcts

• Apply a Bayesian Decision Network with empirical observations to evaluate likelihood of potential outcomes

• Expand the scope of analysis to alternative systems using a generalized framework

• “Softer” Restoration -> Local ordinances (e.g. ferilizer restrictions), Education, etc.
• “Soft” Restoration -> Habitat Creation, Enhancement and Management/Protection Measures
• “Hard” Restoration -> Stormwater BMPs, Point Source Reductions through Time, Regulations

• Can we identify a change in water quality from restoration?
• What data do we have?
• Can we plyr the data to identify a signal?
• Can we plyr the data as input to a BN?

WQ and restoration sites: Spatial match

WQ and restoration sites: Spatial match

WQ and restoration sites: Temporal match

WQ and restoration sites: Spatial match

WQ and restoration sites: Temporal match, before/after

WQ and restoration sites: Spatial match

WQ and restoration sites: Temporal match, before/after, slice

What do the data look like? For one water quality station matched to many restoration sites…

WQ and restoration sites: Temporal match, before/after, slice

# A tibble: 4 x 3
# Groups:   stat [1]
   stat     cmb     cval
  <int>   <chr>    <dbl>
1     7 hab_aft 8.255185
2     7 hab_bef 8.350187
3     7 wtr_aft 8.053273
4     7 wtr_bef 8.129733

What do the data look like? For one water quality station matched to many restoration sites…

WQ and restoration sites: Temporal match, before/after, slice

# A tibble: 4 x 4
   stat     hab     wtr     cval
  <int>  <fctr>  <fctr>    <dbl>
1     7 hab_aft wtr_aft 8.154229
2     7 hab_aft wtr_bef 8.192459
3     7 hab_bef wtr_aft 8.201730
4     7 hab_bef wtr_bef 8.239960

What do the data look like? For many water quality station matched to many restoration sites…

# A tibble: 20 x 4
    stat     hab     wtr      cval
   <int>  <fctr>  <fctr>     <dbl>
 1     6 hab_aft wtr_aft  8.903273
 2     6 hab_aft wtr_bef 11.720206
 3     6 hab_bef wtr_aft 11.902951
 4     6 hab_bef wtr_bef 14.719883
 5     7 hab_aft wtr_aft  8.154229
 6     7 hab_aft wtr_bef  8.192459
 7     7 hab_bef wtr_aft  8.201730
 8     7 hab_bef wtr_bef  8.239960
 9     8 hab_aft wtr_aft 19.867100
10     8 hab_aft wtr_bef 17.444274
11     8 hab_bef wtr_aft 17.331973
12     8 hab_bef wtr_bef 14.909147
13     9 hab_aft wtr_aft  9.030021
14     9 hab_aft wtr_bef  8.621069
15     9 hab_bef wtr_aft  8.398558
16     9 hab_bef wtr_bef  7.989606
17    11 hab_aft wtr_aft  6.576058
18    11 hab_aft wtr_bef  6.727664
19    11 hab_bef wtr_aft  8.112902
20    11 hab_bef wtr_bef  8.264508

What do the data look like? For many water quality station matched to many restoration sites…

What do the data look like? For many water quality stations matched to many restoration sites…

What do the data look like? For many water quality stations matched to many restoration sites…

• In other words, what is the conditional distribution of chlorophyll given restoration type and before/after effect?

• Similar to a two-way ANOVA…

\[ Chl \sim\ f\left(Water \space\ treatment \times Habitat \space\ restoration\right) \]

• This can be extrapolated to additional 'treatments', or a three-way ANOVA

\[ Chl \sim\ f\left(Water \space\ treatment \times Habitat \space\ restoration \times Salinity \right) \]

Conditional distributions on two-levels:

Conditional distributions on three-levels:

Conditional distributions on three-levels:

Conditional distributions on three-levels:

• Water quality (chlorophyll) responds to restoration with varying effects by salinity

• In the frequentist framework - mean chlorophyll varies given treatment

\[ Chl \sim\ f\left(Water \space\ treatment \times Habitat \space\ restoration \times Salinity \right) \]

• In the Bayesian framework - probability of an event depends on occurrence of other events

\[ P\left(Chl \mid Event\right) = \frac{P\left(Event \mid Chl\right) \cdot P\left(Chl \right)}{P \left(Event\right)} \]

What is the probability of low/medium/high chlorophyll given other events?

• Do water quality conditions differ by restoration type?
• Does it differ by salinity as a natural covariate?
• Is the change in agreement with expectation?

BN lets us evaluate likelihood of potential outcomes given conditional distributions

• Next steps (all)